Abstract
The fractional Brownian motion Xβt is the solution of the Sturm–Liouville fractional differential equation of order β, (with β a positive real number), enforced by a zero mean normal white noise. The main aim of this paper is to derive the fractional Fokker–Planck equation (FFP) related to the above fractional differential equation. It is shown that FFP is ruled by the fractional derivative of order 2H, with Hurst index H=β−1/2.This means that the diffusive term in the FFP equation is found. Further studies are necessary for the complete FFP equation in the more general case in which the equation is enforced not only by the white noise, but also by a nonlinear transformation of the response itself.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
